Densified wood – stronger than steel (but…)

Densified wood: In a very recent issue of Nature (Vol 554: 224-228), authors Jianwei Song and others reported that they were able to make wood into a very dense, very strong and tough material.  They removed some of the lignin polymer and carefully crushed the remainder, mostly cellulose.  The density increased from 0.42 grams per cubic centimeter to about three times that, denser than water.  Basically, they collapsed the open conduits of wood, the xylem vessels that carry water and nutrients upward from the soil.  They were able to layer it in alternating directions of the former grain, like plywood.  Its strength (stress needed to break it) exceeds that of even high-strength steel .  Interestingly, its toughness also increased (this is the energy or work needed to break it); ordinarily, toughness goes down as strength increases (e.g., see my post about spider silk).  They had an interesting demo of toughness with a projectile shot into it.

It’s premature to say this will replace steel as a structural material in many applications.  For one, densified wood swells alarmingly at high humidity, by 8.4% after 128 hours in 95% relative humidity.  It’s not dimensionally stable then.  One topic I didn’t see addressed is its anisotropy – its properties vary with the direction of applied stress.  Even layered in alternating directions like plywood, in the third dimension, parallel to the original grains, I’d expect it to be easier to disrupt – to delaminate, as it were.

Densified wood also is not more resilient than steel.  After hitting the highest stress that it can tolerate, it breaks down bit by bit at higher strains (relative extension).

Stay tuned.


Our brains got a lot of mutations while we were in utero

Mutations in our brains as they develop in our time as fetuses: In a very recent issue of Science (Vol. 359: 550-555; 2 Feb. 2018), authors Taejeong Bae and others reported that we accumulate a lot of genetic mutations in our individual brain cells as we develop.   They found different mutations in each cell, and 200 to 400 of them, on average, accumulating over the age of the fetus. They looked for very basic types of mutations, changes of one DNA base for a different one, termed single-nucleotide variants.  (That is, they did not look at mutations that deleted or inserted stretches of DNA.) Nearly half of the mutations occurred in parts of our DNA related to brain function (vs. other organs, though the functions overlapped). Clearly, we still function with these changes in all our neurons.  Granted, many variations in DNA bases don’t affect a protein that the cells make (the genetic code is redundant – several different sets of three bases specify the same amino acid), or, for stretches of DNA that don’t make proteins but interact with genes to regulate their degree of expression, they many not change that regulatory function much.

Still, these mutations are quite abundant – 50 times more per cell than in our adult cells of the liver, colon, and intestine, and almost 1000 times more than in our germ cells (eggs and sperm).  Of course, the latter resistance to mutation is a good thing.  While mutations that don’t disable us or kill us are the source of our evolution of function, including our oversized brains themselves, too many mutations reduce our biological fitness.

The mutations in our young, developing brains resemble those in cancers.  The authors take this to indicate that these “normal” (my word) mutations are part of the background for cancer.  They attribute the high rate of mutation to oxidative stress and to a high rate of cell division (faster is sloppier in copying DNA, then) during the stages called pregastrulation and neurogenesis.

The variations between cells that must occur remind me of quips about the UNIX and Linux operating systems – everyone comes with a different version and claims they’re all equivalent.  I wonder how non-equivalances among neurons affect how we think.

The variations also remind me of the wonder that our extremely complex bodies with so many controls to go awry (hormones, nerves, enzyme complements, basic development) almost always function well or even very well.  I have to skip over the 2/3 or so of conceptions that lead to death of the embryo – some errors are just too big.  We’re the lucky ones.

Subjective time: does time seem faster as we get older?

Here’s a simple (simplistic?) argument that we experience time in logarithmic fashion.

Intro: When we were young, it seemed to take ages to get older – to the next grade in school, to the next stop on a long drive, to wait till Christmas or another holiday.  There are so many cliches about the change in the experience of time as we get older.

The math, with a few graphs: follow this link

Proxima Centauri b – a habitable planet? (No)

Recently, astronomers using the European Southern Observatory telescope in northern Chile, detected a planet orbiting the star nearest to our solar system, Proxima Centauri.  The way they detected the planet, by the tiny wobble it causes the star along our direction of view, is very interesting, though not the topic I’m following up here. The star and its planet are 4.25 light-years away, so, still an extreme distance for any probe to reach that can hit even the highest speeds our spacecraft attain.  Nonetheless, astronomers and their biology/physics colleagues are wondering if this planet can sustain life.

The star is cool but the planet orbits close to it, so that the planet might attain an average temperature near the range in which water is liquid.  Of course, there are many other requirements for being amenable to life, even if only microbial life.  Here is a very detailed write-up, running to 16 pages.

Falling skydiver

A skydiver jumps from a plane. How fast is he or she going at any time? There is a fairly simple expression for the drag on a body falling in air (“body” as a generic in the physics sense, not meaning “dead body!”). One can insert it into a simple differential equation that is “straightforward” to solve by separation of variables; along the way, I prove some useful relations. I also show how far off is the prediction of a simpler form often given for its simpler math.

How cold is that rain?

How cold is that rain?


If you’ve stood outside in the rain, even on a warm day, you’ve felt the chill of the rain. There are two reasons, the first being that water takes up heat from your skin much faster than does air when both the rain and the air are at the same temperature that’s lower than body temperature – the same reason that metal feels cold even when it’s at room temperature or even above.  The second reason is that the rain is at a lower temperature than the air, and we can estimate just how much cooler it is, based on air temperature and relative humidity.  We can also reverse the calculation, to estimate relative humidity from the temperatures of the air and of the rain (catch the rain in an insulated cup).

I present the theory and examples in a PDF document (I wrote it in Word with MathType – too many equations to save and paste into WordPress handily!).  I hope you enjoy it.

You can skip to using the theory to estimate the rain’s temperature from the air temperature, relative humidity, and air pressure.  I created a spreadsheet, in which you can enter the values in either metric or English units.  There is a second section to it, in which you can do the inverse, calculating the relative humidity from the air temperature, rain temperature, and air pressure.

The image attached is, of course, not freely falling rain but rainwater draining from a roof canale on our Southwest style flat roof.  It was intriguing to see how the flow breaks up and shortly generates slightly flattened spheres.

Making spider silk for fun and profit: worth it?

Company using microbes to make spider silk garners $123,000,000 in venture capital.

This is a story reported on the Tech Crunch site, about Bolt Threads.  The proposed uses seem to center on wearable textiles (vs. engineering textiles).  Why spider silk?  It’s touted to be stronger than other polymers – stronger than Teflon, in the Tech Crunch page. That’s a mistake, since they meant Kevlar, the amazing polymer used in bulletproof vests.  Spider silk is also claimed to be stronger than steel.  Consider these points:

  • “Strength” is one of many properties of a structural material (yes, textiles are structures of a special sort); stiffness and toughness are equally important.
  • These properties commonly trade off against each other, and in any application of a material – polymer, steel, carbon fiber, etc. – there are choices to make. Brick is a strong material but it’s very un-tough, as are ceramics in general.  Steels are strong but the strongest steels aren’t the toughest (meaning taking the most energy to break).  I have a quick summary of properties below.
  • Many structural materials have properties that vary with the environment. The steel in WW II Liberty ships became brittle at cold North Atlantic Ocean conditions, and they sometimes broke apart under wave stresses.
  • Spider silk is notorious for its properties depending strongly on humidity and temperature.

Another property of note is resilience.  When stressed (stretched along its length, for example, some spider silk stays stretched.  Not so good for a tie.  Of course, silkworm silk is good here (doesn’t stretch, is stiff), and some types of spider silk are resilient, and stiff, like silkworm silk.  Pick the right type of spider silk, and perhaps blend several types.

  • As many investigators have noted, spider silks vary; some classifications put as many as 27 types in play. Bolt Thread likely will need to make a number of different silks.  Look at orb-weaving spiders, the common web-makers.  They use strong and resilient silk for the main radial lines and nonresilient, sticky silk for the cross lines.  The strong lines keep the web intact, but they would just kick an insect back out rather than trap it.  The sticky lines do the trapping.
    • One use I saw touted the use of spider silk instead of steel cables on aircraft carriers for arresting the landing of an aircraft. Two scenarios seem to have be implied.
      • One is that the trapping type of silk, or flagelliform silk, be used, as if catching a very big fly. As Stephen Vogel notes in his oh-so-readable book, Cats’ Paws and Catapults, spider silk is nonresilient; the energy it would absorb would go into making so much heat that the net would melt. So, that won’t work.
      • The other is using spider silk as the arresting cables, the ones that the aircraft’s tailhook engages, or perhaps the balancing cables that take the shock of stopping a landing aircraft by paying out from a drum with hydraulic damping, like big car shock absorbers. There, the tough and strong silk might be used.  A variant arresting method, for aircraft missing a tailhook, is to put out a big net instead of the arresting cable.  OK, but why go to spider silk, which is likely harder to maintain and in a function where weight is not critical?
    • Spider silk really isn’t stronger than Kevlar. Both (some) spider silk (drag lines) and Kevlar are stronger than steel, and notably better than stell per unit weight, but Kevlar is stronger than spider silk by a factor of 1.5 to 7.  Nothing is better for strength.

    Here’s a rundown of strength, stiffness, toughness, resilience, ductility, and some shape dependence of material failure.   We can conclude at the end that spider silk has a mix of properties that suit it to certain uses, choosing it over Kevlar (or steel, or putty, or ….), but not to other uses.  Using it for high-priced silk ties is an affectation for the rich.  I’ll wait to hear what real uses are in line.

We can look at a graph of the extent to which a material deforms (its fractional change in length) against the stress put on it (the force over an area).  Such a plot is useful for materials that have the same properties in any direction, or isotropic materials, though one can use it for materials whose properties vary by direction, if one specifies the direction.  (There are also differences in stresses applied in one direction, as extension or compression, and shear stresses applied nonuniformly, as in trying to stretch a material into a distorted rectangle or parallelogram.)

Here’s a simple comparison of two materials, well, OK, three.  Material A deforms a lot less than does material B, under the same stress.  Or, you can say that material A takes a lot more stress to deform it by a given amount.  It has greater stiffness.  We can take the slope of stress vs. strain at any point and call it stiffness.  For many materials, stiffness is pretty constant over a range of stress levels – e.g., steel.


Strength is the amount of stress needed to make the material break apart.  Material A isn’t as good as B.


Toughness is the total energy needed to make a material fail.  It’s the area under the curve from zero stress to failure.  Again, B is better.


Resilience is the ability to return to the original shape when stress is relieved.  We tend to like that.  Spring steel needs to be resilient.  Putty is non-resilient, and we like that for keeping it in place once we apply it.  I drew a line on the side of a related but distinct material, A2, indicating what strain remains when the stress goes down.  It ends with a non-zero strain when stress is completely removed.

Material A2 is not fully resilient; it might be resilient, however, from its new, once-stretched state, under later stresses.  If so, we can call the material ductile, able to be deformed and take on a new, resilient state.  It’s what we do in forming metals with dies by stamping, pulling through wire dies, forging, etc.

We can also call resilience elasticity.  The opposite of it is plasticity – undergoing plastic deformation.



I’ve attached another graph with an explicit comparison of spider silk to Kevlar

OK, spider silk is tougher than Kevlar if not stronger and not stiffer (of course, we knew it wasn’t stiffer!).   Its resilience depends on how far you stretch it – probably not as resilient as Kevlar, but close.


Model rocketry – equations and tests

Sort of a one-stop-shop for model rocketry theory, experiments, and data analysis for a high-school class, or an advanced middle-school class such as we have at the Las Cruces Academy:

Tsiolkovsky derived the equation for the final speed of a rocket in free space (no air drag) in 1903!  I have a derivation here, plus an elaboration that goes on to consider air drag and gravity for a surface launch, and another one that looks at how a rocket has to be designed with propellant, payload, and basic infrastructure (the shell, we may say).

Our students at the Las Cruces Academy did rocket launches in the desert, measuring the altitude achieved with geometric measurements.

Some pictures are useful.  Check out the link on the LCA News and Events page.

The results for altitude vs. rocket motor impulse are summarized in a spreadsheet.  Altitude looks to be linear in impulse, in line with numerical simulations I performed.  We had to be very careful with our measurements, btw, since small errors lead to big errors in altitude.

A sideline: where does the kinetic energy go, partitioned between exhaust gases and the rocket?  At burnout for a serious rocket, there’s more in the gases than in the payload that’s left.

Adventures in light propagation – teaching and research

This multilayered post can be followed from one PDF document, or by the explicit links given below in the description of the whole study.  The post covers:

  • Teaching:
    • Working with students to make a light intensity detector using a photodiode.  It measures photon flux density in the visible portion of the electromagnetic spectrum.
    • We went on to use it as the detector in a (spectro)photometer for measuring the concentration of methylene blue dye illuminated with light from a high-intensity yellow LED.
  • Research:
    • The main point I just completed writing up is the use of radiative transport equations that I developed for estimating scattered light within a uniform canopy of plants.    The solutions for the fluxes of a direct beam and diffuse light together are analytic, in term of algebraic and exponential quantities.
    • The model also is useful for simulating the propagation of light inside leaves for modeling photosynthetic rates of leaves with different structures and pigmentations.  I have a number of publications on this (which I can link later, when I find PDFs of them.  One interesting prediction I made is that leaves with half-normal chlorophyll content should allow sharing of light with leaves deeper in a dense canopy, ultimately giving an 8% increase in biomass and yield.  John Hesketh’s group at the University of Illinois tested this in the field and got an 8% increase over fully green leaves! (Pettigrew WT, Hesketh JD, Peters DB, et al. (1989) Characterization of canopy photosynthesis of chlorophyll-deficient soybean isolines. Crop Science 29:1025-1029).
    • Recently (Nov.-Dec 2017) I extended it to multiple layers of different optical properties.  The challenge was testing it rigorously and making a comprehensive explanation with text and equations.

Back toward teaching: I wanted to verify that the photodiode circuit responded linearly to flux density.  I made a simple error in using layer scattering media too close to the detector, invalidating Beers’ law for the direct beam alone.  However, I then dove into the propagation of direct and diffuse light for its inherent interest.

The lead PDF document here has several sections:

  • The most recent inquiry: is the photodiode responding linearly to photon flux density?
  • The radiative transport equations
  • A few notes about extensions to nonuniform canopies

Within the lead document are links to several others.  The links are imbedded within the lead document; the links are also noted directly here:

  • A short write-up of the electronic circuit for the photodiode detector
  • Fixing-approximations.pdf:” A set of notes on improving a whole-canopy flux model (light, CO2 uptake and respiration, transpiration) in the representation of:
    • The enzymatic model of photosynthetic carbon fixation, bridging the cases of high light and low light
    • The equations for radiative transport, with their full derivation and some numerical results
    • A discussion of extensions of the model for leaves varying in absorptivity with depth in the canopy, or that are clumped, or that vary in temperature as they transpire water at different rates
    • In turn, this PDF references a short Fortran 90 program I wrote to solve the radiative transport equations
    • Also, a link to a 2013 publication I had with Zhuping Sheng, modeling all the fluxes of a pecan orchard.  The relevance is that I cited in this second PDF the modeling of light in a regular array of tilted, ellipsoidal canopies of individual trees.  Sheng did the experimental measurement of fluxes with eddy covariance equipment. I modeled the results, with one surprising finding that pecan trees, unlike every other plant I’ve studied, do not reduce its stomatal conductance and thus its transpiration in very dry conditions.  They operate at high transpiration rates and poor water-use efficiency in these conditions.
    • A couple of references to publications:
      • A model of radiative transport in layered plant canopies represented by finite layers (a finite-element model), as an integral equation that’s readily solved numerically.   I cite this publication because within it I discuss the changing angular distribution of diffuse light with depth.
      • The clever method of colleague and friend Michael Chelle and his former advisor Bruno Andrieu for radiative transport in an arbitrary assemblage of light-scatters.  The method is called nested radiosity, accounting essentially exactly for nearby scatterers affecting light at a given leaf and then via a nice smoothing approximation (mean field) for more distant scatterers.


You make more heat than the Sun

Say what?  The sun’s temperature is surely very much higher than our temperature – in fact, in absolute units, it is nearly 20 times hotter (nearly 5800 Kelvin, in scientific units, while we’re less than 310 Kelvin, or K).  The sun is also considerably bigger than any one of us, or all of us. Its mass is about 330,000 times the mass of our own earth, and the earth’s mass is about 86 sextillion times (86 x 1021) more than our tiny little 70 kg or 154 pounds apiece.  Yet the statement in the title is true in one important sense: the average kilogram of our body generates more metabolic heat than the average kilogram of the sun.


One way to get at this figure is that, at rest, we put out about 70 Watts, less than the (fortunately less and less common) 100 W incandescent light bulb.  Still, we’re at 1 watt (W) per kilogram.  We eat to maintain that rate.  Over an hour, that 70 W amounts to an energy use of 70 x 3600 Joules.  Now, a Joule is 0.242 calories and a food calorie (Cal) is 1000 of the standard calories, so in that hour we metabolize about  65 Cal. Over a 24-hour day, we then need 24 x 65 = 1560 Cal…well, more like 2,000 if we’re minimally active or 10,000 if we’re top-notch mountain climbers or skiing across Antarctica.


How much power, which is energy per unit time, does the sun put out?  By the time sunlight reaches the surface of the earth, its peak at noon is as high as 1000 Watts on a square meter; that’s a hair-dryer’s worth, for every square meter (a bit bigger than a square yard).  Above our atmosphere, it’s higher, about 1360 W per square meter.  It gets more intense as we get closer to the sun.   You can search a book or the Internet for the inverse-square law to find out how much more intense.  Using the fact that we are, on average, 150 million km (93 million miles) from the sun and the sun’s diameter is close to 1,390,000 km (870,000 miles), we can calculate the intensity at its “surface” (remember, no hard surface – it’s a gas bag).  It’s 46,000 times greater than at our distance, or about 63 million watts per square meter, compared to our 70 Watts per 2 square meters of skin surface.  Let’s go on.  Over its whole surface, the sun radiates energy to space.  That surface area is 4 π times the sun’s radius squared, or 6.07 quintillion square meters (6.07 x 1018).  This is 2.36 trillion square miles, if you’d like old English units, and that’s close to a million times the area of the US.  Multiply this by the output per square meter, to get 382 septillion W (3.82 x 1026).  Divide that by the mass of the sun, which is nearly 2,000,000,000,000,000,000,000,000,000,000 kg (or 2 x 1030 in easier notation).  The sun puts out a measly 0.00019 Watts per kg.  You expend 5,000 times more, on a mass or “weight” basis.


This low output from the sun is a good thing, so that the sun does not run out of its nuclear fuel in less than its long life of about 10 billion years.  Other stars are much brighter and burn up much faster, in as little as a few million years.  Compared to the sun, we are profligate in using energy…which we capture from the sun through our crops and pastures.  The plants on earth use only 0.3% of the solar energy reaching us, and we capture as food only several percent of what they capture.  This low capture rate can only be helped a little, and it’s why there can’t be too many more of us.